Selection bias has long been central in methodological discussions across epidemiology and other fields. In epidemiology, the concept of selection bias has been continually evolving over time. In this issue of the Journal, Mathur and Shpitser (Am J Epidemiol. XXXX;XXX(XX):XXXX-XXXX) present simple graphical rules for using a Single World Intervention Graph (SWIG) to assess the presence of selection bias when estimating treatment effects in both the general population and a selected sample. Notably, the authors examine the setting in which the treatment affects selection, an issue not well-addressed in the existing literature on selection bias. To place the work by Mathur and Shpitser in context, we review the evolution of the concept of selection bias in epidemiology, with a primary focus on the developments in the last 20-30 years since the introduction of causal directed acyclic graphs (DAGs) to epidemiologic research.

In causal mediation analysis, nonparametric identification of the natural indirect effect typically relies on, in addition to no unobserved pre-exposure confounding, fundamental assumptions of (i) so-called \"cross-world-countterfactuals\" independence and (ii) no exposure-induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend existing bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data from the Harvard PEPFAR program in Nigeria, where we evaluate the extent to which the effects of antiretroviral therapy on virological failure are mediated by a patient\'s adherence, and show that inference on this effect is somewhat sensitive to model assumptions.

Several methods have been proposed for partially or point identifying the average treatment effect (ATE) using instrumental variable (IV) type assumptions. The descriptions of these methods are widespread across the statistical, economic, epidemiologic, and computer science literature, and the connections between the methods have not been readily apparent. In the setting of a binary instrument, treatment, and outcome, we review proposed methods for partial and point identification of the ATE under IV assumptions, express the identification results in a common notation and terminology, and propose a taxonomy that is based on sets of identifying assumptions. We further demonstrate and provide software for the application of these methods to estimate bounds. Supplementary materials for this article are available online.